and  the  Magnetic  Relations  of  the  Heavenly  Bodies.        451 
Such  a  physical  cause,  which,  according  to  our  theory,  must 
necessarily  change  periodically  the  magnetic  condition  of  the 
sun,  is  really  present ;  I  mean  the  periodically  changing  quantity 
of  suu-spots. 
In  my  discussion  of  the  law  of  rotation  of  the  sun  and  that 
of  the  large  planets*,  I  have  shown  theoretically  that  the  presence 
of  sun-spots  on  the  sun's  surface  must  generate  essential  but 
regular  modifications  of  the  law  of  rotation.  These  modifica- 
tions have  been  proved  to  exist  by  the  observations  of  Sporer; 
so  that  I  have  succeeded  in  giving  for  the  modified  law  a  theo- 
retical formula  which  represents  more  accurately  the  observed 
states  than  the  empirical  formula  of  Sporer. 
The  essential  character  of  the  law  of  rotation  changed  at  the 
time  of  sun-spot  maximum,  and  the  causes  which  produce  the 
alterations,  were  explained  by  me  (/.  c.  p.  82)  in  the  following 
words : — 
"At  the  time  of  the  sun-spot  maximum  the  polar  currents  are 
considerably  retarded  in  consequence  of  the  increased  friction ; 
these  currents  will  therefore  arrive  at  the  equator  with  a  much 
smaller  velocity  than  they  do  at  the  time  of  a  sun-spot  minimum. 
Hence  at  the  times  of  sun-spot  maxima  the  accelerating  effect 
of  the  deeper  strata  of  the  sun's  surface  must  be  much  larger 
than  at  the  time  of  a  minimum  ;  and  for  this  reason  the  observed 
velocity  of  rotation  at  the  equator  must  be  greatest  at  the  time 
of  a  maximum — just  as  is  shown  by  Sporer' s  observations." 
P.  85.  "  As  we  have  seen,  all  the  observations  of  Sporer  can  be 
much  better  represented  by  the  above  theoretical  formula  than 
by  his  own  empirical  formula.  Excluding  the  observations  for 
the  immediate  neighbourhood  of  the  equator,  the  sum  of  the 
least  squares  of  errors  for  Sporer's  formula  is  85 •  2,  for  mine 
4-4-8,  or  little  more  than  half  of  the  value  for  Sporer' s  formula. 
H  The  derived  theory  of  the  law  of  rotation,  even  near  the  time 
of  a  maximum  of  sun-spots,  has  therefore  been  confirmed  by 
Sporer's  observations;  and  the  above  formula  will  therefore 
have  to  be  regarded  in  future  as  a  quite  general  expression  for 
the  modifications  of  that  law." 
It  is  therefore  a  necessary  consequence  of  my  theory  that  at  the 
times  of  sun-spot  maxima  the  relative  velocity  and  the  friction  of 
the  currents  is  increased-,  and  hence  the  intensity  of  the  electrical 
currents  produced,  as  well  as  the  magnetism  of  the  sun,  is  greatest 
at  those  times. 
At  the  times  of  sun-spot  maxima  the  mechanical,  electrical, 
and  magnetical  energy  present  in  the  sun  is  increased  at  the 
expense  of  a  certain  quantity  of  heat. 
*  Proc.  of  Roy.  Saxon  Soc.  Sci.  Feb.  11,  1871. 
2G2 
